PLANE TRIGONOMETRY. 61 



7. If ft y be angles, unequal and less than TT, which sutiMy 

 the equation 



cos a cos x sin a sin x _ 1 



~T~ " c ' 



then will (6 8 -f c 8 - a 8 ) cos/3 cos y + (c*+ a*- b*) sin /3 sin y = a*+ 6"- c*. 



278. If a, ft be angles, unequal and less than TT, which satisfy 

 the equation 



a cos 2x + b sin 2a; = 1, 



and if (I cos' 2a + m sin 8 2a) (/ cos 8 2/3 + m sin' 2/3) 

 = {/ cos 2 (a + ft) + m sin' (a + ft) J 8 , 



then will either = ?>&, or a*b*= 



m + l 



II. Identities and 



.. If tan'^i = 1 + 2 tan',5, then will cos 25 = 1 + 2 cos 2.1 . 



280. Having -given that sin (B + C-A\ sin (C + A - 7?), 

 I + - (7) are in A. p. ; prove that tan -4, tan , tan C are in 



A. P. 



281. Having given that 



prove that (P~y) t (y-<*), or (a-)8) is an odd multij.lt of TT. 



282. it ,-,,to, cot/?, cot y be in A. P., so also will cot(/?-a), 

 cot()3-y). . 



283. Having given 

 co80 = coaa cos/?, c< 



/J=(seoa-l)(8eca-l). 



6 ff S 

 C08& ooe 0^ 006 a cos ft, tan-tanjr = tan 



